Forward Only Learning for Orthogonal Neural Networks of any Depth

Fuente: arXiv
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Main Authors: Caillon, Paul, Colagrande, Alex, Fagnou, Erwan, Delattre, Blaise, Allauzen, Alexandre
Format: Preprint
Published: 2025
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author Caillon, Paul
Colagrande, Alex
Fagnou, Erwan
Delattre, Blaise
Allauzen, Alexandre
author_facet Caillon, Paul
Colagrande, Alex
Fagnou, Erwan
Delattre, Blaise
Allauzen, Alexandre
contents Backpropagation is still the de facto algorithm used today to train neural networks. With the exponential growth of recent architectures, the computational cost of this algorithm also becomes a burden. The recent PEPITA and forward-only frameworks have proposed promising alternatives, but they failed to scale up to a handful of hidden layers, yet limiting their use. In this paper, we first analyze theoretically the main limitations of these approaches. It allows us the design of a forward-only algorithm, which is equivalent to backpropagation under the linear and orthogonal assumptions. By relaxing the linear assumption, we then introduce FOTON (Forward-Only Training of Orthogonal Networks) that bridges the gap with the backpropagation algorithm. Experimental results show that it outperforms PEPITA, enabling us to train neural networks of any depth, without the need for a backward pass. Moreover its performance on convolutional networks clearly opens up avenues for its application to more advanced architectures. The code is open-sourced at https://github.com/p0lcAi/FOTON .
format Preprint
id arxiv_https___arxiv_org_abs_2512_20668
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Forward Only Learning for Orthogonal Neural Networks of any Depth
Caillon, Paul
Colagrande, Alex
Fagnou, Erwan
Delattre, Blaise
Allauzen, Alexandre
Machine Learning
Artificial Intelligence
Backpropagation is still the de facto algorithm used today to train neural networks. With the exponential growth of recent architectures, the computational cost of this algorithm also becomes a burden. The recent PEPITA and forward-only frameworks have proposed promising alternatives, but they failed to scale up to a handful of hidden layers, yet limiting their use. In this paper, we first analyze theoretically the main limitations of these approaches. It allows us the design of a forward-only algorithm, which is equivalent to backpropagation under the linear and orthogonal assumptions. By relaxing the linear assumption, we then introduce FOTON (Forward-Only Training of Orthogonal Networks) that bridges the gap with the backpropagation algorithm. Experimental results show that it outperforms PEPITA, enabling us to train neural networks of any depth, without the need for a backward pass. Moreover its performance on convolutional networks clearly opens up avenues for its application to more advanced architectures. The code is open-sourced at https://github.com/p0lcAi/FOTON .
title Forward Only Learning for Orthogonal Neural Networks of any Depth
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2512.20668